Cluster density

What makes WiFi faster at home than at a coffee shop? How does Google order its search results from the trillions of webpages on the Internet? Why does Verizon charge $15 for every GB of data we use? Is it really true that we are connected in six social steps or less?
These are just a few of the many intriguing questions we can ask about the social and technical networks that form integral parts of our daily lives. This course is about exploring the answers, using a language that anyone can understand. We will focus on fundamental principles like “sharing is hard”, “crowds are wise”, and “network of networks” that have guided the design and sustainability of today’s networks, and summarize the theories behind everything from the social connections we make on platforms like Facebook to the technology upon which these websites run.
Unlike other networking courses, the mathematics included here are no more complicated than adding and multiplying numbers. While mathematical details are necessary to fully specify the algorithms and systems we investigate, they are not required to understand the main ideas. We use illustrations, analogies, and anecdotes about networks as pedagogical tools in lieu of detailed equations.
All the features of this course are available for free. It does not offer a certificate upon completion.

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從本節課中

Influencing People in Social Networks

In this lesson, we will continue with our theme of influence, now paying more attention to people's social networks. We will discuss different ways of measuring importance and a popular model for influence spread in social networks like Facebook and Twitter.

教學方

Christopher Brinton

Lecturer

Mung Chiang

Professor

腳本

Now let's try to formulate some of the intuition as to why we're not able to break through the Eve, George, Frank, and Hannah state of being not flipped. So, we could call cluster any group of nodes that have connections among themselves. So taking any group of nodes with connections we can take them and say, here's a cluster, right? So, in this graph, let's call Eve, George, Frank, and Hannah a cluster. What we want to do is find the density of that cluster cluster density. In order to find the cluster density, what we first do is we first find for each node, the fraction of neighbors that are inside the cluster. So, for Eve, that's 3 over 5 which is 60%. [SOUND] For Frank that's 3 over 4, which 75%. [SOUND] George has 100%, all three of them are in there and same thing for Hannah, 100%. Now the smallest of these fractions. We take the smallest of them, which is 60%, and that's going to be the density. So, in this case, 60%, is the cluster density. So, we find the cluster density, we go, for each node, we find the fraction of neighbors that are inside the cluster. And the smallest of these fractions is the density. So, the smallest of them is given the weakest link. And we take the weakest link to be the density because that's what's going to tell us whether or not it's possible to flip the cluster or not. We need at least the threshold outside of the cluster in order to be able to penetrate it, which should make sense. So, in this case we have 60% is inside this cluster here, right? So the density is 60%. Which means that there's only 40% of the density outside of it. Meaning, you know, and we, we, we know that Eve is our way in, in this case. But, only 40% of the density is outside of the cluster, which is not high enough. And therefore, since 40% is less than the threshold, which is 50%, there's no possible way for us to penetrate this. Because there's only 40% influence [NOISE] on this cluster. Given that all the other nodes outside of it are already flipped. So therefore, it is impossible to penetrate this cluster. So, the key take away here is that in general, we need at least thresholds to be outside of the cluster in order to penetrate it. So, we would need this to be at least 50% being outside in order for us to flip Eve. So, if Eve had, for instance another link outside here, then we'd have exactly 50% outside, and then we couldn't penetrate that cluster. [BLANK_AUDIO]